The present invention relates to an apparatus and method used for subjecting information data to an error-correcting coding and a modulation such as a run length limited (“RLL”) modulation to create channel data, recording the channel data onto a recording medium, and subjecting channel data reproduced from the recording medium to a demodulation, such as an RLL demodulation, and an error-correcting decoding to reconstruct the information data, and more particularly to a recording-medium reproducing apparatus, a decoding method, a decoding program, and a program-recorded medium containing the decoding program.
Among error-correcting methods, the turbo code method and the low density parity check (“LDPC”) code method have been capturing the spotlight mainly in the communication field by virtue of its having such high performance as to approach the theoretical limit of the transmission rate at which transmission can be achieved without errors (namely, Shannon limit). Further, studies on applications of the turbo code method and the LDPC code method to the recording medium field as well as the above-noted communication field, have energetically been presented.
A recording and reproducing apparatus using this turbo code is explained briefly. FIG. 17 is a schematic diagram of a recording and reproducing apparatus as a first background art, which performs coding and decoding processes of turbo codes. A turbo coder 1 performs turbo coding on inputted information data ui to output code data ci. An RLL modulator 2 performs RLL modulation on the inputted code data ci to output modulated data mi. A pre-coder 3 performs non-return-to-zero inverse (“NRZI”) conversion on the inputted modulated data mi to output channel data ai. The channel data ai outputted in this way is transmitted to a partial response (“PR”) channel 4. This PR channel 4 has a property that adjacent channel data ai interfere with each other. As a result of this, an intersymbol interference occurs to a reproduced signal y′i reproduced from the PR channel 4. Also, the channel data ai, when passing the PR channel 4, undergoes deformation such as noise addition, band limiting or crosstalk. Therefore, the reproduced signal y′i reproduced from the PR channel 4 has errors added thereto. It is noted here that a symbol with a prime (′) indicates that the symbol is data reconstructed after reproduction (that is, indicating addition of errors by the PR channel 4), and a symbol without a prime (′) indicates that the symbol is data before recording.
In the case where the PR channel 4 is a recording medium, i.e., in the case of a system which performs recording and reproduction on media such as magnetic recording, magneto-optical recording and optical recording, there exist constraints such as band limiting of the PR channel 4, intersymbol interference, clock synchronization and the like. Therefore, the RLL method is usually used for the modulation. Generally, RLL data is expressed as RLL(d, k), where “d” and “k” represent minimum and maximum run lengths of 0's in a modulated data sequence. The run length restriction on the modulated data sequence is called “RLL condition.”
Describing the RLL in more detail, polarity inversion intervals of recording waveform sequences or trains are limited to a minimum polarity-inversion interval Tmin and a maximum polarity-inversion interval Tmax. That is, inversion intervals T of recording waveform trains are within the limits of Tmin≦T≦Tmax. Generally, the minimum polarity-inversion interval Tmin is expressed as (d+1)×Tw. The maximum polarity-inversion interval Tmax is expressed as (k+1)×Tw. It is noted here that “Tw,” which denotes the width of a detection window for reproduced signals, is equal to the greatest common measure of polarity-inversion intervals, i.e., Tw=η×Tb, where “Tb” denotes a data interval before modulation, and the symbol “η,” called a coding rate, is equal to m/n. That is, pre-modulation m bits are transformed into post-modulation n bits.
Moreover, if a polarity per polarity-inversion interval T is expressed by one bit like “0” or “1”, then a recording waveform train is equal to a channel data train. The channel data train is expressed, for example, as “ . . . 011100001111111100111 . . . ” In this channel data train, a series of succeeding “0” bits or a series of succeeding “1” bits has a bit length of not less than (d+1) and not more than (k+1). Hence, a constraint concerning the channel data is also called RLL condition. More specifically, the RLL condition can be expressed as a constraint concerning modulation data. Moreover, the RLL condition can also be expressed as a constraint concerning channel data.
A PR channel a posteriori probability (“APP”) detector 5, to which the reproduced signal y′i is inputted, performs an a posteriori probability decoding in compliance with constraints concerning channel data ai, pre-codes and a PR transfer characteristic, and outputs a logarithmic likelihood ratio L(m′i) relating to modulation data m′i.
An APP decoder 6 for RLL modulation, to which the logarithmic likelihood ratio L(m′i) of the modulation data m′i from the PR-channel APP detector 5 is inputted, performs an a posteriori probability decoding in compliance with the constraint concerning RLL modulation, and outputs a logarithmic-likelihood ratio L(c′i) relating to coded data c′i.
A turbo decoder 7 performs a turbo decoding in compliance with the constraint concerning turbo codes placed by the turbo coder 1, and outputs a logarithmic-likelihood ratio L(u′i) relating to information data u′i. Thus, the logarithmic-likelihood ratio L(u′i) of the information data u′i outputted from the turbo decoder 7 is binarized by a comparator 8 and outputted as reconstructed information data u′i.
A detailed description regarding the operation principle of a recording and reproducing apparatus employing turbo codes according to the first background art is found in, for example, “Turbo coded RLL constrained optical recording channels with DVD minimum mark size”, Optical Data Storage Topical Meeting 2001, pp. 91–93, April 2001 (Literature 1), and “Turbo Decoding with Run Length Limited Code for Optical Storage”, Japanese Journal Applied Physics, Vol.41 (2002) pp. 1753–1756, Part 1, No. 3B, March 2002 (Literature 2).
However, in the demodulation corresponding to the RLL modulation performed in the recording and reproducing apparatus, input modulation data is soft information and output coded data is also soft information as with the case of the APP decoder 6 for RLL modulation, which necessitates execution of a soft decoding. Herein, the term “soft decoding” refers to the decoding in which the coding results are outputted in the form of probabilities of being “0” or “1” (likelihood). Such processing for performing the demodulation for RLL modulation (hereinbelow, referred to as RLL demodulation) through the soft decoding requires an extremely large calculating amount. This increases the size of an RLL demodulation circuit.
Accordingly, there has been proposed a recording and reproducing apparatus which can reduce an RLL demodulation processing amount to be lower than that in the recording and reproducing apparatus shown in FIG. 17. FIG. 18 is a schematic view showing a reproducing apparatus as second background art. The reproducing apparatus performs iterative decoding processing. Moreover, FIG. 19 is a schematic view showing a recording apparatus for transmitting channel data reproduced by the reproducing apparatus shown in FIG. 18 to a PR channel. Description will be first given of the recording apparatus with reference to FIG. 19.
A first RLL modulator 11 performs the RLL modulation upon inputted information data u′i and outputs primary modulation data m1i. The primary modulation data m1i is then inputted into a primary pre-coder 12 and a systematic error-correcting coder 13. The primary pre-coder 12 performs the NRZI conversion upon the primary modulation data m1i to generate primary channel data a1i and outputs it to a multiplexer 16. The systematic error-correcting coder 13 performs the systematic error-correcting coding on the inputted primary modulation data m1i to generate and output checking data pi. A second RLL modulator 14 performs the RLL modulation on the inputted checking data pi to output a secondary modulation data m2i. A secondary pre-coder 15 performs the NRZI conversion on the inputted secondary modulation data m2i to generate a secondary channel data a2i and outputs it to the multiplexer 16.
The multiplexer 16 multiplexes the primary channel data a1i received from the primary pre-coder 12 and the secondary channel data a2i received from the secondary pre-coder 15 to generate channel data ai and outputs it to a PR channel 17.
Description is now given of the reproducing apparatus shown in FIG. 18. Data y′i reproduced by the PR channel 17 is inputted to a PR channel APP detector 21. Then, in compliance with constraints concerning channel data, pre-codes and a PR transfer characteristic, the a posteriori probability decoding is performed and a logarithmic likelihood ratio L(m′i) relating to modulation data m′I is outputted. A multiplexer 22 decomposes the logarithmic-likelihood ratio L(m′i) of the modulation data m′i and divides the data into a logarithmic-likelihood ratio L(m1′i) relating to primary modulation data and a logarithmic-likelihood ratio L(m2′i) relating to secondary modulation data. The logarithmic-likelihood ratio L(m1′i) relating to primary modulation data is inputted into an adder 24, while the logarithmic-likelihood ratio L(m2′i) relating to secondary modulation data is inputted into an APP decoder 23 for RLL modulation.
Generally, an APP decoder has 2-input and 2-output terminals, i.e., an information input terminal u;I into which the likelihood relating to information data is inputted, a code input terminal c;I into which the likelihood relating to code data is inputted, an information output terminal u;O from which the likelihood relating to information data is outputted, and a code output terminal c;O from which the likelihood relating to code data is outputted. The APP decoder, receiving inputs of the likelihood relating to information data and the likelihood relating to code data, updates those likelihoods in compliance with a constraint concerning codes. It is to be noted that likelihoods inputted to the information input terminal u;I are called a priori information. From the information output terminal u;O, likelihoods regarding information data are outputted as a posteriori probability decoding results. From the code output terminal c;O, likelihoods regarding code data are outputted as the a posteriori probability decoding results. Herein, the term “information data” refers to data inputted to a coder corresponding to an APP decoder, and the term “code data” refers to data outputted from the coder.
Moreover, the APP decoder can be expressed as a 1-input and 1-output block if a priori information regarding the information data is not inputted thereto and code data is not outputted therefrom as an a posteriori probability decoding result, i.e., if the information input terminal u;I and the code output terminal c;O are not provided. Receiving inputs of the likelihood relating to code data, this 1-input and 1-output APP decoder performs the a posteriori probability decoding in compliance with the constraint regarding codes and outputs the likelihood relating to information data. Such a 1-input and 1-output APP decoder is embodied by, for example, the PR-channel APP detector 21 and the APP decoder 23 for RLL modulation shown in FIG. 18.
Further, if the error-correcting codes are systematic error-correcting codes, the APP decoder for these systematic error-correcting codes has 2-input and 2-output terminals. The 2-input and 2-output terminals of the APP decoder for the systematic error-correcting codes are sometimes embodied in different forms. That is, the input terminals are composed of an information input terminal u;I into which likelihoods regarding information data are inputted, and a checking input terminal p;I into which likelihoods regarding checking data are inputted. The output terminals are composed of an information output terminal p;O from which likelihoods regarding information data are outputted, and a checking output terminal c;O from which likelihoods regarding checking data are outputted. Herein, the term “systematic code” refers to such a code that information data (i.e., input data) is contained as it is in code data (i.e., output data). Among the output data (code data), data other than the input data (information data) (i.e., a redundancy generated by coding) is called checking data. Such APP decoders include, for example, an APP decoder 28 for error-correcting codes that will be described later with reference to FIG. 18.
In FIG. 18, the APP decoder 23 for RLL modulation, into which the logarithmic-likelihood ratio L(m2′i) relating to the secondary modulation data is inputted, performs the RLL demodulation through the a posteriori probability decoding processing, and outputs a logarithmic-likelihood ratio L(p′i) relating to checking data p′i.
The adder 24, into which the logarithmic-likelihood ratio L(m1′i) relating to the primary modulation data m1′i is inputted, further adds extrinsic information L2,ext(m1′i) inputted from a later-described second subtracter 27 and outputs a result as a priori information L1,a(m1′i) regarding the primary modulation data m1′i.
Receiving inputs of the a priori information L1,a(m1′i) regarding the primary modulation data from the adder 24, an APP decoder 25 for RLL condition performs the a posteriori probability decoding in compliance with an RLL condition, and outputs a logarithmic-likelihood ratio L1,post(m1′i) relating to primary modulation data. The RLL condition can be expressed by a trellis diagram. For example, FIG. 20 is a trellis diagram showing the RLL condition in (1, 7)RLL modulation. In FIG. 20, bits “0” and “1” given to transmission branches extending from internal states S0–S7 at a point k to internal states S0–S7 at a point (k+1) represent modulation data. The RLL condition in this (1, 7)RLL modulation is: a minimum run length d=1, and a maximum run length k=7.
The trellis diagram shown in FIG. 20 has eight internal states of from “S0” to “S7”. In this case, the point “k” is updated every bit of modulation data. A path that satisfies the trellis diagram is, for example, “. . . 010010001000000010100 . . . ”. The RLL condition regarding modulation data in the (1, 7)RLL modulation is a constraint that a run of “0” bits between consecutive “1” bits must have a length of at least d and not more than k, i.e., a bit length of at least 1 and not more than 7. In other words, the APP decoder 25 for RLL condition performs a decoding based on the trellis diagram representing the RLL condition concerning modulation data.
A first subtracter 26 subtracts the extrinsic information L2,ext(m1′i) regarding primary modulation data outputted from the second subtracter 27 from the logarithmic-likelihood ratio L1,post(m1′i) relating to primary modulation data inputted from the APP decoder 25 for the RLL condition, and outputs a result as a logarithmic-likelihood ratio L1,ext(m1′i) relating to primary modulation data.
In the APP decoder 28 for error-correcting codes, the logarithmic-likelihood ratio L1,ext(m1′i) from the first subtracter 26 is inputted into the information input terminal u;I, while the logarithmic-likelihood ratio L(p′i) from the APP decoder 23 for RLL modulation is inputted into the checking input terminal p;I, and the logarithmic-likelihood ratio L2,post(m1′i) relating to primary modulation data is outputted from the information output terminal u;O. It is to be noted that the checking output terminal p;O from which logarithmic-likelihood ratios regarding checking data are outputted is not connected to any terminal.
The second subtracter 27 is fed with the logarithmic-likelihood ratio L2,post(m1′i) relating to primary modulation data m′i that is outputted from the information output terminal u;O of the APP decoder 28 for error-correcting codes, and the logarithmic-likelihood ratio L1,ext(m1′i) relating to primary modulation data m′i from the first subtracter 26. Then, the second subtracter 27 subtracts the logarithmic-likelihood ratio L1,ext(m1′i) from the logarithmic-likelihood ratio L2,post(m1′i), and outputs a result as extrinsic information L2,ext(m1′i) regarding primary modulation data to the first subtracter 26 and the adder 24.
Thus, between two APP decoders, i.e., the APP decoder 25 for RLL condition and the APP decoder 28 for error-correcting codes, the iterative decoding is performed by repeatedly delivering logarithmic-likelihood ratios regarding the primary modulation data. By this iterative decoding, errors of later-described reconstructed primary modulation data m1′i can be decreased.
A comparator 29 binarizes the logarithmic-likelihood ratio L2,post(m1′i) relating to primary modulation data outputted from the information output terminal u;O in the APP decoder 28 for error-correcting codes, and outputs obtained binarized values as reconstructed primary modulation data m1′i to an RLL demodulator 30. Consequently, the RLL demodulator 30 performs the RLL demodulation on reconstructed primary modulation data m1′i and finally outputs a result as reconstructed information data u′i. At this point, the RLL demodulator 30 performs a hard decoding involving inputting and outputting of binarized hard information. This drastically reduces a computing amount of soft decoding processing, allowing achievement of a smaller-sized demodulation circuit for RLL modulation.
A detailed description regarding the operation principle of a recording and reproducing system involving the iterative decoding according to the second background art is found in “Constrained Coding Techniques for Soft Iterative Decoders”, Global Telecommunications Conference 1999, pp. 723–727.
However, the recording and reproducing system in the second background art has the following problems. That is, as described above, two APP decoders for executing iterative decoding are the APP decoder 25 for RLL condition and the APP decoder 28 for error-correcting codes. Among these, the APP decoder 25 for RLL condition performs the APP decoding in compliance with a constraint concerning a run length limit among the constraints concerning the RLL modulation. This implies that the decoding processing adopting iterative decoding would not contain a constraint concerning a PR transfer characteristic. As a result, decoding processing in the above recording and reproducing system in compliance with the constraint concerning the PR transfer characteristic is executed only once in the PR-channel APP detector 21.
In other words, in the above recording and reproducing system, decoding is not executed through iterative adoption of the constraint concerning the PR transfer characteristic. This causes deterioration of the error rate of reconstructed information data u′i, thereby posing a problem of decreased recording density of a recording medium such as the PR channel 17. Moreover, there is also a problem that stricter tolerances are required for the recording medium and the recording and reproducing system.
Herein, the term “tolerances” refers to allowable errors in parameters that would cause increases in errors of reconstructed information data. The parameters with respect to the tolerances to the recording medium are exemplified by warpage expressed by tangential tilts or radial tilts, substrate noise, and the like. Further, when the recording medium is an optical disk, the parameters also include thickness errors of a cover glass, refractive index, birefringence index, and the like. On the other hand, the parameters with respect to the recording and reproducing apparatus include, for example, a detracking amount of a tracking servo, recording power, and the like. Furthermore, when the recording and reproducing apparatus is a recording and reproducing apparatus adopting the optical recording or magneto-optical recording scheme, the parameters further include aberrations of objective lenses, offsets of the focusing servo (defocus amount), reproducing power, and the like.